An introduction to the thermodynamic and macrostate levels of nonequivalent ensembles

2004/04/26 by Hugo Touchette, H. Touchette, Richard S. Ellis +3 · 14 citations
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physa.2004.03.088

published as Physica A 340, 138-146, 2004. · Revtex4, 5 pages, 1 figure

openalex publication_date 2004/04/26 · arxiv created 2004/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This short paper presents a nontechnical introduction to the problem of nonequivalent microcanonical and canonical ensembles. Both the thermodynamic and the macrostate levels of definition of nonequivalent ensembles are introduced. The many relationships that exist between these two levels are also explained in simple physical terms.

Cited by

• Ensemble equivalence for general many-body systems
• Partial equivalence of statistical ensembles and kinetic energy
• Nonanalyticities of Entropy Functions of Finite and Infinite Systems
• Generalized canonical ensembles and ensemble equivalence
• Simple spin models with non-concave entropies
• Nonequivalence of Ensembles for Long-Range Quantum Spin Systems in Optical Lattices
• Ensemble inequivalence in the ferromagneticp-spin model in random fields
• On the interpretations of Tsallis functional in connection with Vlasov–Poisson and related systems: Dynamics vs thermodynamics
• Nonequivalence of ensembles in the Curie–Weiss anisotropic quantum Heisenberg model
• Many-body spin glasses in the microcanonical ensemble
• The specific heat anomaly stems from a third-order phase transition in the 2D lattice sine-Gordon model
• Ensemble inequivalence and Maxwell construction in the self-gravitating ring model
• Equivalence of ensembles for two-species zero-range invariant measures
• Microcanonical entropy of the spherical model with nearest-neighbour interactions

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